Password Safe has an excellent pedigree: The original version of this password database was designed by security expert Bruce Schneier. The current version follows the design path laid down in the early 2000s--and that's a problem, because user needs have moved on.
Password Safe is a solid tool for storing, organizing, and searching for passwords, but it sits outside the browser environment. You must constantly switch back and forth between it and the browser. While you can connect a Password Safe entry to an associated website, this still requires you to leave the browser, bring up the Password Safe application, and launch the site from the appropriate entry, using the "Browse to Entry And Autotype" command (or use Ctrl-T, which is explained in the documentation, but which does not appear as a shortcut in the right-click menu).
There are many good things about Password Safe. It's open source, which not only means it's free, but it means the code can be inspected by thousands of people who can verify that it works as promised and that there is nothing hidden. Given recent revelations about the degree to which much security software has been compromised, this is not a trivial aspect of the product. Autotype uses a default syntax to handle this. Some sites might not follow this pattern, but there are extensive customization options you can set on a specific entry, handled via a string of embedded commands, such as using \m to enter the email address associated with the entry. You can also vary the timing of commands, or specify lines from the "notes" entry to be used as part of the command string. This is a high level of flexibility, but it's a bit clunky compared to more tightly integrated applications.
The interface design, while dated, is perfectly functional, clean, and generally intuitive. (I noticed one bug: When I added a group, an item changed its name to the name of the group. This cleared itself up when I forced the tree to refresh again.) A user can set various actions for double-click, shift-double-click, and run, allowing a high degree of customization.
While every user can benefit from better password management, Password Safe is a tool for more technical users, especially those whose needs don't entirely revolve around their favorite browser. I can see Password Safe being useful for managing logins to multiple console window sessions, for example. In addition, it is immune to functionality loss due to changes in browser specification or how plug-ins or extensions are handled. Lastly, the fact that it is free makes it an option for anyone for whom even the less expensive commercial programs are still out of reach.